Progress in FY 2006 has been in the following areas: (1) We have continued structural studies of amyloid fibrils. We have completed a revised structural model for beta-amyloid fibrils, in which all basic aspects of the structure are determined by experimental data. This model applies to fibrils grown with gentle agitation. We have also developed improved techniques for preparing beta-amyloid fibrils under quiescent conditions, such that the fibrils have homogeneous morphologies and clean NMR spectra. A three-fold symmetric structural model for these quiescently grown fibrils, supported by NMR data on chemical shifts, intermolecular dipole-dipole couplings, and sidechain-sidechain contacts, is near completion. We have also begun structural studies of fibrils formed by the islet amyloid precursor protein (a.k.a. amylin). In our amylin project, we have developed efficient protocols for synthesizing and purifying the peptide, as well as protocols for preparing fibrils with uniform morphologies and high-quality solid state NMR spectra. We have obtained a full set of 13C chemical shifts for amylin fibrils and have measured intermolecular dipole-dipole couplings, supporting a parallel beta-sheet structure that is apparently quite similar to the structure of agitated beta-amyloid fibrils. (2) We have continued structural studies of a 40-residue peptide from HIV-1 Vpu, containing its transmembrane segment, in phospholipid bilayers. Using a novel form of two-dimensional solid state NMR, we have identified intermolecular contacts between transmembrane helical segments in Vpu oligomers. These contacts allow us to develop experimentally-based models for the supramolecular structure of oligomeric Vpu ion channels. We have completed solid state NMR measurements on HIV-1 Rev fibrils and Rev/RRE RNA coaggregates, which demonstrate that the Rev protein structure is essentially unchanged upon interaction with RRE RNA. (3) We have developed new solid state NMR methods, including a new approach to selective measurement of specific interatomic distances between carbon-13 labels in samples that contain uniformly-labeled amino acids. This new approach to selective distance measurements seems likely to facilitate a wide range of structural studies by solid state NMR. In an extension of this approach, we are using stochastic modulation of dipolar recoupling in solid state NMR to permit the measurement of purely distance-dependent nuclear spin polarization exchange rates in uniformly labeled molecules. (4) We have begun solid state NMR studies of the structures of two yeast prion proteins in their filamentous states, namely Ure2p and Sup35. Data to date indicate that Sup35NM and Ure2p(1-89) both form in-register parallel beta-sheets in their amyloid fibrils, that approximately half of the Ure2p(1-89) sequence may be disordered in the fibrils, and that both the N and M domains of Sup35NM participate in beta-sheet formation.